Mode spectra of thermally excited two-dimensional dust Coulomb clusters.

The mode spectra of finite Coulomb clusters, confined systems of charged microspheres in a complex plasma, have been determined experimentally. The spectral power density of all possible modes has been measured for particle numbers between N=3 and N=145 under different plasma conditions. The agreement between measured and calculated mode frequencies is found to be very good. From this, the parameters of the particle interaction, like particle charge and screening strength, have been extracted quantitatively. In addition, the particle and mode temperatures have been obtained. The modes and the particles show the same temperature and the principle of equipartitition holds for these systems. Moreover, certain modes of interest have been compared among the different clusters, as there are the breathing mode and intershell rotation as well as the lowest- and highest-frequency modes. Moreover, the mode-integrated spectrum shows two broad maxima which are explained from "shearlike" or "compressionlike" modes. From this analysis, the transition from finite number to crystal-like properties is observed to occur around N=12 particles. Finally, a model to visualize the transition from normal mode oscillations to wave dispersions in a 2D lattice has been proposed.